Hit or Miss Sports is introducing a new product this year. If its see-at-night s
ID: 2761062 • Letter: H
Question
Hit or Miss Sports is introducing a new product this year. If its see-at-night soccer balls are a hit, the firm expects to be able to sell 68,000 units a year at a price of $50 each. If the new product is a bust, only 48,000 units can be sold at a price of $45. The variable cost of each ball is $20, and fixed costs are zero. The cost of the manufacturing equipment is $7.8 million, and the project life is estimated at 10 years. The firm will use straight-line depreciation over the 10-year life of the project. The firm’s tax rate is 35%, and the discount rate is 12%.
Hit or Miss Sports can expand production if the project is successful. By paying its workers overtime, it can increase production by 43,000 units; the variable cost of each ball will be higher, however, equal to $25 per unit. By how much does this option to expand production increase the NPV of the project? (Assume the probability the see-at-night soccer balls will be a hit is 50%).
Explanation / Answer
If the new project is a hit
Contribution margin per unit = Selling price - Variable cost = $50 - $20 = $30 per unit
Contribution margin = $30 * 68,000 units = $2,040,000
Annual depreciation = $7,800,000 / 10 = $780,000
Net income = $2,040,000 - $780,000 = $1,260,000
Free cash flow = Net income after taxes + Depreciation = $1,260,000 * (1 - 0.35) + $780,000 = $819,000 + $780,000 = $1,599,000
Present value of annuity factor = {1 - (1+r)-n}/r
Present value of annuity factor (PVAF) for $1 at 12% for 10 years = (1-1.12-10)/0.12 = 5.6502
Present value of annuity of free cash flows = $1,599,000 * 5.6502 = $9,034,669.80
Net present value = -Initial investment + Present value of free cash flows = -$7,800,000 + $9,034,669.80 = $1,234,669.80
If the new project is a bust
Contribution margin per unit = Selling price - Variable cost = $45 - $20 = $25 per unit
Contribution margin = $25 * 48,000 units = $1,200,000
Annual depreciation = $7,800,000 / 10 = $780,000
Net income = $1,200,000 - $780,000 = $420,000
Free cash flow = Net income after taxes + Depreciation = $420,000 * (1 - 0.35) + $780,000 = $273,000 + $780,000 = $1,053,000
Present value of annuity of free cash flows = $1,053,000 * 5.6502 = $5,949,660.60
Net present value = -Initial investment + Present value of free cash flows = -$7,800,000 + 5,949,660.60 = $1,850,339.40.
Net present value of project = NPV if project is hit + NPV if project is bust = ($1,234,669.80 * 50%) + ($0 * 50%) = $617,334.90
If the project is expanded
Contribution margin per unit = Selling price - Variable cost = $50 - $25 = $25 per unit
Contribution margin = $25 * 111,000 units = $2,775,000
Annual depreciation = $7,800,000 / 10 = $780,000
Net income = $2,775,000 - $780,000 = $1,995,000
Free cash flow = Net income after taxes + Depreciation = $1,995,000 * (1 - 0.35) + $780,000 = $1,296,750 + $780,000 = $2,076,750
Present value of annuity of free cash flows = $2,076,750 * 5.6502 = $11,734,052.85
Net present value = -Initial investment + Present value of free cash flows = -$7,800,000 + $11,734,052.85 = $3,934,052.85.
Increase in NPV of the project due to expansion = $3,934,052.85 - $617,334.90 = $3,316,717.95
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